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Mathematics for science and technology

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# 1 Chance and probability

‘Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.’

(George Boole, 1815–1864)

In many branches of science it is not possible to predict with any certainty what the outcome of a particular event will be. There may be several possible outcomes and all the scientist can offer in the way of quantitative prediction is an assessment of the relative likelihood of each of these outcomes. For example, if a man and a woman both carry the cystic fibrosis gene without showing symptoms of the disease, the chances are 1 in 4 that their first child will suffer from the condition. Such assessments of probability are a routine part of genetics, nuclear physics, quantum physics and many other scientific disciplines.

In seeking to understand the nature and rules of probability it is often best to focus initially on everyday examples that are easily visualised. So Section 2 to Section 5 feature many examples of tossed coins and rolled dice. However, you will also get the opportunity to see how these ideas are applied to some genuine scientific problems: for example, what is the probability that two people planning to have a child will both turn out to be carriers of the cystic fibrosis gene?